采用拉普拉斯尺度混合先验的结构化近似消息传递算法

Structured Approximate Message Passing Algorithm with a Laplacian Scale Mixture Prior

为了准确有效地实现自然图像的压缩感知重构,提出一种使用拉普拉斯尺度混合(Laplacian Scale Mixture,LSM)先验的结构化近似消息传递(Approximate Message Passing,AMP)算法.利用LSM模型构建AMP算法的高阶统计约束,将压缩感知重构问题转化为先验信息估计问题和奇异值最小化问题.首先,用LSM分布刻画相似块矩阵奇异值的稀疏性,其中该稀疏性指示了图像块的相似性,因此LSM模型被用来描述图像的非局部相似结构;然后,通过期望最大化算法估计LSM模型的尺度参数,得到可靠的先验信息;最后,由AMP算法求解奇异值最小化问题,实现图像的精确重构.实验结果表明,提出的结构化AMP算法的图像重构质量优于多种主流的压缩感知图像重构算法.

In order to reconstruct natural images from compressive sensing(CS)measurements accurately and effectively,a novel structured approximate message passing algorithm using a Laplacian scale mixture(LSM)prior is proposed.The higher-order statistical constraint of the AMP algorithm is created by the LSM model,turning the CS recovery problem into a prior information estimation problem and a singular value minimization problem.Firstly,we use the LSM distribution to model the sparsity of the singular values of the matrices built by similar patches,which denotes the similarity of image patches,and thus utilize the LSM model to describe the nonlocal similarity of images.Secondly,to obtain reliable prior information,the scale parameters of the LSM model are estimated through the use of the expectation-maximization(EM)algorithm.Finally,the singular value minimization problem is solved by the AMP algorithm to achieve the accurate image reconstruction.Experimental results show that the reconstruction quality of our structured AMP algorithm is superior to the state of art CS reconstruction algorithms.